\begin{frame} \frametitle{Derivatives of Basic Functions} \begin{exampleblock}{} Compute the following derivative: \begin{talign} \frac{d}{dx} &(12x^5 - 10x^3 - 6x + 5) \\ &\mpause[1]{= 12\frac{d}{dx} (x^5) - 10\frac{d}{dx} (x^3) - 6\frac{d}{dx} (x) + \frac{d}{dx} (5) }\\ &\mpause[2]{= 12\cdot 5x^4 - 10 \cdot 3x^2 - 6\cdot 1 + 0 } \mpause[3]{= 60x^4 - 30x^2 - 6 } \end{talign} \end{exampleblock} \pause[5]\medskip \begin{exampleblock}{} The motion of a particle is given by: \begin{itemize} \item $s(t) = 2t^3 - 5t^2 + 3t + 4$ \quad($t$ is in seconds, and $s(t)$ in cm) \end{itemize} Find the acceleration function, and the acceleration after $2s$. \pause\smallskip \begin{talign} v(t) &= \frac{d}{dt} s(t) = \mpause[1]{6t^2 - 10t + 3} && \mpause[4]{\text{in cm/s}}\\ \mpause[2]{a(t) }&\mpause[2]{= \frac{d}{dt} v(t) = \mpause[3]{12t - 10}} &&\mpause[5]{\text{in cm/s$^2$}} \end{talign} \pause\pause\pause\pause\pause\pause The acceleration after $2s$ is $14\text{cm}/\text{s}^2$. \end{exampleblock} \end{frame}